$A$ $B$ $C$ If: $ BC = 4x + 8$, $ AC = 40$, and $ AB = 8x + 8$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 8} + {4x + 8} = {40}$ Combine like terms: $ 12x + 16 = {40}$ Subtract $16$ from both sides: $ 12x = 24$ Divide both sides by $12$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $BC$ $ BC = 4({2}) + 8$ Simplify: $ {BC = 8 + 8}$ Simplify to find ${BC}$ : $ {BC = 16}$